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A136662
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Number of cycles of the permutations of [1,2,...,n], for n=1,2,3,...
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1
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1, 2, 1, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 5, 4, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The row lengths sequence is A000142(n), n>=1, (factorials).
The permutations of [1,2,...,n] are ordered in the standard way (lexicographic or numerically increasing). E.g. in Maple as permute(n) list for not too large n (around 10).
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LINKS
| W. Lang, First rows and cycle decompositions.
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FORMULA
| a(n,k)= number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.
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EXAMPLE
| [1];[2,1];[3,2,2,1,1,2];[4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2];...
Row n=3: permutations of [1,2,3] in the order [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]. Cycle decomposition: [[[1], [2], [3]], [[1], [2, 3]], [[1, 2], [3]], [[1, 2, 3]], [[1, 3, 2]], [[1, 3], [2]]]. Number of cycles: [3,2,2,1,1], the entries of row n=3.
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CROSSREFS
| Row sums (total cycle numbers) A000254.
Sequence in context: A021473 A035181 A035151 * A023595 A177718 A057515
Adjacent sequences: A136659 A136660 A136661 * A136663 A136664 A136665
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Feb 22 2008, May 21 2008
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